WebPart.AllowConnect property
SharePoint 2013
Gets or sets a value that indicates whether the WebPart control allows other controls to form connections with it.
Assembly: Microsoft.SharePoint (in Microsoft.SharePoint.dll)
This property cannot be personalized by individual users. The value of its WebPartStorageAttribute is Storage.Shared, which specifies that the property will be stored with the same value for all users. Only users with the Write web pages right can set this property. It can be set programmatically, or it can be set through the Web Part task pane in the shared view of the Web-based user interface, or by using a SharePoint Foundation–compatible HTML editor, such as SharePoint Designer.